If $a,c
eq 0$ and $\alpha,\beta$ are the roots of the equation $ax^{2} + bx + c = 0$, then the quadratic equation with $1/\alpha$ and $1/\beta$ as its root is

Question

If $a,c 
eq 0$ and $\alpha,\beta$ are the roots of the equation $ax^{2} + bx + c = 0$, then the quadratic equation with $1/\alpha$ and $1/\beta$ as its root is

Dr. Abubacker · Accepted Answer

(b)
Here, $\alpha + \beta = - \frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$
Sum of the given roots$= \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha\beta} = - \frac{b}{c}$
And product of the given roots$= \frac{1}{\alpha}.\frac{1}{\beta} = \frac{a}{c}$
$	herefore$Required equation is
$x^{2} -$(sum of roots)$x +$product of roots=0
$\Rightarrow x^{2} + \frac{b}{c}x + \frac{a}{c} = 0$
$\Rightarrow \ \ cx^{2} + bx + a = 0$

Q. If $a,c \neq 0$ and $\alpha,\beta$ are the roots of the equation $ax^{2} + bx + c = 0$, then the quadratic equation with $1/\alpha$ and $1/\beta$ as its root is

Explanation

Reviewed by Dr. Abubacker

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